Permanent magnet synchronous motors (PMSMs) are utilized in various applications because they have generally favorable efficiency characteristics relative to other types of motors. Typically, PMSMs have three separate electrical windings within the stator which are each powered by alternating current (AC) voltages Va, Vb, and Vc. In operation, the winding currents Ia, Ib, and Ic each oscillate at a frequency proportional to the rotor speed and are separated by 120 degrees in phase from one another. These winding currents induce a rotating magnetic field which may be out of phase with the rotor. The resulting shaft torque depends upon both the magnitude of the magnetic field and the phase angle relative to the rotor. The magnetic properties of the permanent magnets are impacted by temperature which impacts the resulting torque. Accurate torque delivery requires compensation for the effects of temperature.
For convenience, the winding voltages and currents may be represented by vectors with respect to a rotating reference frame that rotates with the rotor. The mapping between rotor position and the rotating reference frame depends upon the number of poles in the motor. The voltage vector has a direct component Vd and a quadrature component Vq. Similarly, the current has a direct component Id and a quadrature component Iq. Vd, Vq, Id, and Iq do not oscillate based on rotor position.
In certain applications, such as electric vehicles and hybrid electric vehicles, electrical power is available from a non-oscillating direct current (DC) voltage source such as a battery. Therefore, inverters are utilized to convert the non-oscillating voltage Vdc into three oscillating voltages. Inverters contain a discrete number of switching devices and are therefore capable of supplying only a discrete number of voltage levels at each of the three motor terminals. For a 2-level inverter, at any moment in time, the switching devices are set to electrically connect each of the three AC motor terminals to either the positive or the negative DC terminal. Thus, eight switching states are available. Two of these switching states, in which all three AC terminals are connected to the same DC terminal, are called zero states. In the remaining six states, one AC terminal is connected to one of the DC terminals and the other two AC terminals are connected to the opposite DC terminal. The inverter is capable of switching rapidly among these eight states.